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In this paper, for the first time, we introduce a Belief Propagation (BP)-based distributed trust and reputation management algorithm. The proposed algorithm can be utilized in many distributed systems from Peer-to-peer (P2P) networks to social and mesh networks. In this work, we focus on P2P networks and explore the application of BP-based trust and reputation management in a decentralized environment in the presence of malicious peers. In a typical P2P trust and reputation management system, after each transaction, the client peer (who receives a service) provides its rating about the quality of the service provided by the server peer for that transaction. In such a system, we view the problem of trust and reputation management as to compute two sets of variables: 1. the reputation parameters of peers based on their quality of service, and 2. the trustworthiness parameters of peers based on the ratings they provide after each transaction. We distinguish between these two parameters as a peer might provide high quality service as a server while providing malicious ratings as a client. The proposed scheme, referred to as BP-P2P, relies on the BP algorithm in an appropriately chosen factor graph representation of the P2P network. The reputation and trustworthiness parameters are computed by a BP-based distributed message passing algorithm between the peers on the factor graph. We provide a detailed evaluation of BP-P2P via analysis and computer simulations. We show that BP-P2P is very robust in computing trustworthiness values and filtering out malicious ratings. Specifically, we prove that BP-P2P iteratively reduces the error in the reputation values of peers due to the malicious ratings with a high probability. Further, comparison of BP-P2P with some well-known and commonly used P2P reputation management techniques (e.g., EigenTrust and Bayesian Framework) indicates the superiority of the proposed scheme in terms of robustness against malicious behavior. We also s- ow that the computational complexity of BP-P2P grows only linearly with the number of peers and the communication overhead of BP-P2P is lower than the well-known EigenTrust algorithm.